The second-order Van-Leer MUSCL schemes are actually one of the most
popular high order schemes for fluid dynamic computations. In the frame
work of the Euler equations, we introduce a new slope limitation
procedure to enforce the scheme to preserve the invariant region: namely
the positiveness of both density and pressure as soon as the associated
first order scheme does it. In addition, we obtain a second-order
minimum principle on the specific entropy and second-order entropy
inequalities. This new limitation is developed in the general framework
of the MUSCL schemes and the choice of the numerical flux functions
remains free. The proposed slope limitation can be applied to any change
of variables and we do not impose the use of conservative variables in
the piecewise linear reconstruction. Several examples are given in the
framework of the primitive variables. Numerical 1D and 2D results are
performed using several finite volume methods.